# Vega / Vol / Value

This option trading mini-game will test your understanding of vega, implied volatility and option value and how they are all related. Let’s see an example.

Old imp vol: 69.51

Old value: 25.477

New imp vol: 69.41

New value: ???

Vega: 13.57

In this mini-game we are given the old and the new implied volatility levels, the old option value and the vega of the option. Our challenge is to calculate the new option value. All of the questions in this mini-game involve re-arranging the basic formula for vega.

## Vega = Change in option value / Change in implied volatility

The change in option value is just the new value minus the old value. Likewise the change in implied volatility is just the new implied vol minus the previous implied vol.

Re-arranging;

**Change in option value = Vega * Change in implied volatility**

Change in option value = 0.1357 * (69.41 – 69.51)

= -0.014

So the option falls by 0.014 ticks in value. Therefore the **new value is 25.463**.

Notice that the vega was given as 13.57. This is the normalized vega, which means the vega for a 1% change in implied vol. We need to multiply this by 0.01 to give us the change per cent rather than per dollar.

Make sure you understand what these numbers really mean and are not just re-arranging formulae to get the answer! The vega tells us how big an impact a change in implied volatility has on an option’s value. So to know the change in option value you multiply the vega by the amount of the change in implied volatility. Some of the questions in this mini-game ask for you to calculate the implied volatility levels given the vega and the changes in option value. In those case, you divide the change in option value by the vega to arrive at the change in the volatility level.

## How option vega is used in the real option markets

This mini-game aims to teach you how changes in implied volatility and change in option value are related. The vega of an option tells us how close the relationship is. A larger option vega means that an option’s value is more sensitive to changes in implied volatility. If you can play this mini-game successfully, you will understand how the two are related.

In the real option markets, this relationship is vital to option traders. It reveals a trader’s exposure to movements in implied volatility. It also tells how a *difference in option value translates into a difference in implied volatility.* For example, suppose an option with 5 vega is trading 10 cents above the trader’s theoretical option value. This is equivalent to the option trading 2 implied vols above his theoretical value. Now suppose another option on the same underlying with the same expiration has only 3 vega and is trading 4.5 cents over theoretical value. This option is only trading 1.5 implied vols above the theoretical value. So, in implied volatility terms, this options is **cheaper** than the first option. Option traders use the relationship between vega, implied vol and option theoretical value constantly to relate the prices and values of options to one another in a consistent manner.

## Want to practise trading implied volatility and options?

Why not start a FREE trial of Volcube and you can play this mini-game and several others. Find out more.

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